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svetoff [14.1K]
2 years ago
11

Given cosθ = 3/5, find the five other trigonometric function values. 15

Mathematics
1 answer:
saw5 [17]2 years ago
6 0

cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \impliedby \textit{let's now find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{5^2-3^2}=b\implies \sqrt{25-9}=b\implies \sqrt{16}=b\implies 4=b \\\\[-0.35em] ~\dotfill

sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{5}}\qquad \qquad tan(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\qquad \qquad cot=\cfrac{\stackrel{adjacent}{3}}{\underset{opposite}{4}} \\\\\\ sec(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{adjacent}{3}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}

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Suppose ∠A and ∠B are complementary angles, m∠A = (3x + 5)°, and
mario62 [17]
         m∠A + m∠B = 90
(3x + 5) + (2x - 15) = 90
(3x + 2x) + (5 - 15) = 90
                  5x - 10 = 90
                      + 10  + 10
                         5x = 100
                          5      5
                           x = 20

m∠A = 3x + 5
m∠A = 3(20) + 5
m∠A = 60 + 5
m∠A = 65

m∠B = 2x - 15
m∠B = 2(20) - 15
m∠B = 40 - 15
m∠B = 25
6 0
3 years ago
Read 2 more answers
Where is 10/3 pi on the unit circle?
Tatiana [17]

Answer:

600 degrees

10pi/3 rad = 10pi/3 / pi × 180° = 600 degrees.

4 0
3 years ago
Please Help! Show all the steps!
likoan [24]

You can start by subtracting different equations from each other.

3x + 2y + 3z = 1

subtract

3x + 2y + z = 7

2z = -6

divide by 2

z = -3

add the following two expressions together:

3x + 2y + z = 7

3x + 2y + 3z =1

6x + 4y + 4z = 8

subtract the following two expressions:

6x + 4y + 4z = 8

5x + 5y + 4z = 3

x - y = 5

^multiply the whole equation above by 3

3x - 3y = 15

subtract the following two expressions:

3x - 3y = 15

3x + 2y = 10

-5y = 5

divide each side by -5

y=-1

take the following expression from earlier:

x - y = 5

substitute y value into above equation

x - - 1 = 5

2 negatives make a positive

x + 1 = 5

subtract 1 from each side

x = 4

Therefore x = 4, y = -1, z = -3

I checked these with all 3 equations and they worked :)

(it's quite complicated, comment if you don't understand anything) :)

7 0
3 years ago
A circular running track is 1/4 mile long. Elena runs on this track completing each lap in 1/4 of an hour. What is Elena's runni
daser333 [38]

Answer:

She is going 1mph

Step-by-step explanation:

each lap is 1/4 of a mile and 1/4 of an hour so 4 laps = 1 mile and in 1 hour

7 0
3 years ago
According to the property √a/√b= √a/√b, which choice is equivalent to the quotient below?
garik1379 [7]

Answer:

B

Step-by-step explanation:

\frac{\sqrt{125} }{\sqrt{5}} =\frac{\sqrt{25.5} }{\sqrt{5} } =\frac{5\sqrt{5} }{\sqrt{5} } =5

If you don't understand, you can ask.

4 0
3 years ago
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